5.78 option_willowtree

Function File: value = option_willowtree (CallPutFlag, AmericanFlag, S, X, T, r, sigma, dividend, dk, nodes, path_static)

Computes the price of european or american equity options according to the willow tree model.
The willow tree approach provides a fast and accurate way of calculating option prices. This implementation of the willow tree concept is based on following literature:

• ’Willow Tree’, Andy C.T. Ho, Master thesis, May 2000
• ’Willow Power: Optimizing Derivative Pricing Trees’, Michael Curran, ALGO RESEARCH QUARTERLY, Vol. 4, No. 4, December 2001

Example of an American Call Option with continuous dividends:
(365 days to maturity, vector with different spot prices and volatilities, strike = 8, r = 0.06, dividend = 0.05, timestep 5 days, 20 nodes): option_willowtree(1,1,[7;8;9;7;8;9],8,365,0.06,[0.2;0.2;0.2;0.3;0.3;0.3],0.05,5,20)

Variables:

• CallPutFlag: Call: ’1’, Put: ’0’
• AmericanFlag: American option: ’1’, European Option: ’0’
• S: stock price at time 0
• X: strike price
• T: time in days to maturity
• r: annual risk-free interest rate (cont, act/365)
• sigma: implied volatility of the stock price
• dividend: continuous dividend yield, act/365
• dk: size of timesteps for valuation points (default: 5 days)
• nodes: number of nodes for willow tree setup. Number of nodes must be in list [10,15,20,30,40,50]. These vectors are optimized by Currans Method to fulfill variance constraint (default: 20)
• path_static: Optional: path to static files (required for saving Willowtree transition probabilities)

See also: option_binomial, option_bs, option_exotic_mc.